The claim
The owner, at U36, on the residual of A35: “your account of frustration measured relative to options for an update to meet or fail requirements has me wondering if Arrow’s Impossibility Theorem might be useful to us.” And: “Maybe also cryptography? Reminds me of the two generals problem.” A36 relocated Arrow (“I would locate it slightly differently from the frustration residual”) and drew a table of three obstructions:
- Feasibility: no admissible transformation lies in every constituent’s acceptance set (TERM-060).
- Aggregation: the organization’s rule for combining constituents’ rankings of the admissible transformations yields no coherent choice: under pairwise majority, an alternative that no other beats.
- Epistemic coordination: an admissible, unanimously preferred joint action cannot be guaranteed under the participants’ information and communication constraints.
Each can occur without the other two.
The three constructions
1. Feasibility alone. CASE-115: two operators share one parameter θ, with demands L₁ = (θ − 1)² < 1 and L₂ = (θ + 1)² < 1. Since L₁ + L₂ = 2θ² + 2 ≥ 2, no θ meets both. Everything is known to both, and nothing is communicated. The aggregation is coherent: with two operators, pairwise majority strictly prefers x to y only when both do, which is the Pareto relation, and it is acyclic, so on any finite menu of updates some update is unbeaten. A36: “A system can have no common improving update and still have a perfectly coherent rule for choosing among compromises.”
2. Aggregation alone. A36 §2A’s profile: operators 1, 2, 3 rank updates A, B, C as A ≻ B ≻ C, B ≻ C ≻ A and C ≻ A ≻ B. Each operator’s acceptance condition is that the update be one of A, B, C, so all three lie in every acceptance set and the demands are jointly realizable. Pairwise majority prefers A to B, B to C and C to A (two to one each time), so every option is beaten and the rule yields no choice. Information is complete and the operators share one site.
3. Epistemic coordination alone. Only operator 1 learns whether the moment to act has come. Both rank “act together when it has, and neither act otherwise” above every other outcome, and acting together is admissible. The only channel between them can lose any message. The coordinated attack result (Akkoyunlu et al. (1975); Halpern and Moses (1990) in terms of common knowledge) says no protocol guarantees that both act or neither does while also acting in some run. The argument, in brief: take a run in which the moment has come, every message is delivered and both act, with k messages delivered before acting. Remove the last delivered message. Its sender cannot tell the two runs apart, so it still acts, and so, to keep agreement, must the other. Repeat k times to reach a run with no message delivered in which both act. Operator 2’s view in that run is the same as in the run where the moment has not come and nothing is delivered, in which neither may act; so operator 2 acts there too, which the protocol forbids. There is no infeasibility and no disagreement to aggregate.
A36’s further reading, not part of the claim
A36 §5: “Some obstructions are not interchangeable, and some cannot be eliminated by additional computing power. For example, more accurate gradients do not resolve a genuine conflict of authority. A better voting rule cannot make an infeasible combination of objectives achievable. And better encryption does not overcome an unreliable channel’s lack of guaranteed delivery.” That no remedy for one obstruction removes another is argued from the independence, not shown by it: a remedy might act on two at once. It is interpretive and held here as A36’s.
Two points bear on it.
- Information escapes Arrow but not every aggregation failure. A36 §2D read Sen (NOTE-263) as saying the dual mapping model should “explicitly represent which kinds of information endorsement procedures may use”, since interpersonal comparability breaks Arrow’s impossibility. THEORY-027 shows a failure it does not break: decisive jurisdiction for two constituents, weak Pareto and an unrestricted domain conflict “even when choice need only yield a best element”, and comparability does not remove it. That is CLAIM-353.
- Commitments fix timing only. A36 §4: a cryptographic commitment solves “the timing and integrity of the prediction”, not the scoring, which is CLAIM-340.
A36 also named Arrow’s theorem (Arrow (1950)): with three or more alternatives and an unrestricted domain, no rule gives a complete transitive social ordering satisfying weak Pareto, independence of irrelevant alternatives and nondictatorship. Construction 2 is its standard witness, not its proof. The record holds Arrow only through Sen (NOTE-263) and O’Donnell’s Fourier proof (LIT-346).
What it does not say
- That the three are independent under every choice of demands. An aggregation failure can be recoded as a feasibility failure by adding a demand on the procedure, “the choice is beaten by no majority”, which no option meets in construction 2. The independence holds when the demands are the constituents’ own acceptance conditions and the procedure is held separately, as A37 recommended: “treat the selection of one actual action as a separate governance operation.”
- That they do not interact. A36: “They can reinforce each other, but they are analytically independent.”
- That the operators are agents with rights. A36: “Network modules aren’t automatically moral agents, and their optimization preferences are not equivalent to individual rights.”
Note of 2026-10-29: Halpern and Moses, read
Halpern and Moses, LIT-1213, is now read (NOTE-1381). Construction 3’s argument is their informal induction of §4 and the formal one of Theorem 5. Two precisions.
- The right result. The construction demands “both act or neither does”, with no simultaneity. That is their Proposition 10’s eventual case, with Theorem 9, not Corollary 6’s simultaneous one. Both hold over a lossy channel, so the construction is covered, but the citation should be Proposition 10 with Theorem 9.
- The attribution. The paper credits the problem to Gray (1978) and cites Gallager (1979) and Yemini and Cohen (1979) for proofs. It does not cite Akkoyunlu, Ekanadham and Huber (1975), LIT-1214, which the record files as the standard first source. The 1975 attribution above rests on later usage, not on this paper. LIT-1214 is Unfetched, so it has not been checked.
Their Theorem 8 strengthens the obstruction: unreliable channels are not needed, since any uncertainty in timing blocks common knowledge and with it any guaranteed simultaneous action. The claim is unchanged.
Note of 2026-10-29: Akkoyunlu, Ekanadham and Huber, read
Akkoyunlu, Ekanadham and Huber, LIT-1214, which the note above calls Unfetched, is now read (NOTE-1410). They do state the problem. Their Appendix tells it as two groups of gangsters and a messenger who may be mugged on any trip, with a goal that the plan is delivered and that “both parties know that they are in mutual agreement” that it was, and proves by a shortest-sequence argument that no finite exchange reaches it: “The sequence is infinite even when none of the messages are actually lost.” So the body’s citation of Akkoyunlu et al. (1975) is right as to priority over Gray (1978). This corrects the note above, which said the 1975 attribution rests on later usage: it rests on the paper. One precision. Their goal is mutual knowledge of delivery, with action only as motive, so the step from it to “no protocol guarantees that both act or neither does” is Halpern and Moses’s (LIT-1213), not theirs. The claim is unchanged.